Quantum Zeno and anti-Zeno paradoxes

Continuous observation of a time independent projection operator is known to prevent change of state (the quantum Zeno paradox). We discuss the recent result that generic continuous measurement of time dependent projection operators will in fact ensure change of state: an anti-Zeno paradox.     

Small volume limits of 2-d Yang-Mills

By examining the lattice gauge approximation we show that the small volume limit of the 2-dimensional Yang-Mills functional integral is the natural symplectic measure on the moduli space of flat connections.     

Influence of distributed solid-phase reactions on deflagrations in confined porous propellants

Combustion processes in energetic materials are often modeled by a surface gasification reaction followed by a distributed gaseous flame. However, under confinement, deflagrations in porous or granular propellants are generally accompanied by an increasing pressure difference, or overpressure, between the burned-gas region and the unburned reactants deep within the pores of the material. As the overpressure and/or the solid-phase reaction rate become sufficiently large, the gaseous and solid reaction zones tend to merge into a single multiphase reaction region. Furthermore, in certain parameter regimes, the gas flame penetrates into the porous solid, resulting in subsurface gaseous combustion. When the activation energies of the gaseous and solid-phase reactions are of the same order of magnitude and/or the overpressure becomes significant, gasification reactions may also become active within the solid, thus eliminating a distinct propellant surface and forming a distributed multiphase reaction layer. A large activation-energy analysis of this scenario is presented to study the effects of distributed solid reactions on the deflagration structure and the burning-rate response. The burning-rate eigenvalue is obtained from a numerical solution of the reaction-zone problem, and the results are calculated for various overpressures as well as different gas-to-solid activation-energy and thermal conductivity ratios. It is observed that increasing overpressure results in a more spatially distributed solid-phase reaction and a rapidly increasing flame-propagation speed.     

粉粒体两相流的电容层析成象测量

粉粒体系统中的固相浓度分布的在线测量是十分困难的问题．电容层析成象技术是一种近年来发展起来的非侵入式快速浓度场测量技术．它不干扰流场，不受流动中颗粒浓度、加速度、不透明等因素的制约．本文讨论其测量原理、应用、近期进展、存在的主要问题及其解决的对策．     

ac Conductivity of mixed spinel NiAl0.7Cr0.7Fe0.6O4

ac Conductivity measurements are carried out across the metal to insulator transition in NiAl_0.7Cr_0.7Fe_0.6O₄. The low frequency data is analyzed using Summerfield scaling theory for hopping conductivity. The exponent of the scaling behavior has significantly different values in the conducting and insulating regimes. The hopping frequency and the zero frequency conductivity are found to increase with temperature, slowly in the metallic regime and rapidly in the insulating regime.     

Functional determinants and geometry

Summary In this paper we study the zeta-function determinant in the context of elliptic boundary value problems. Our main technique is to relate the determinant of an operator, or a ratio of determinants, to the boundary values of the solutions of the operator. This has the advantage of restricting attention to the solutions of the operator, which do not depend on the boundary conditions and can often be written down explicitly, rather than the eigenvalues, which are usually difficult to work with. In addition, the problem is reduced to a calculation over the boundary of the manifold which is a closed manifold of dimension one less than the original manifold. This has special significance in the case that the manifold is a finite interval. In this case the boundary is a pair of points and the determinant of an ordinary differential operator is expressed in terms of the determinant of a finite matrix.The results are then applied to some geometric operators. In Sect. 4 we study the Jacobi operator acting along a geodesic segment and the covariant derivative operator acting along a loop. In Sect. 2 we calculate the determinant of the Laplacian acting on sections of a flat bundle over a flat torus. This can be related to an Eisenstein series and thus we have presented a new geometric method of summing such series. This sum is known as Kroneker's Second Limit formula. We then consider operators on a product manifoldM×S ¹.     

Self-assembled monolayers of alkylphosphonic acid on GaN substrates

In this paper we describe the formation and characterization of self-assembled monolayers of octadecylphosphonic acid (ODPA) on epitaxial (0001) GaN films on sapphire. By immersing the substrate in its toluene solution, ODPA strongly adsorbed onto UV/O 3-treated GaN to give a hydrophobic surface. Spectroscopic ellipsometry verified the formation of a well-packed monolayer of ODPA on the GaN substrate. In contrast, adsorption of other primarily substituted hydrocarbons (C n H 2 n+1 X; n = 16-18; X = -COOH, -NH 2, -SH, and -OH) offered less hydrophobic surfaces, reflecting their weaker interaction with the GaN substrate surfaces. A UV/O 3-treated N-polar GaN had a high affinity to the -COOH group in addition to ODPA, possibly reflecting the basic properties of the surface. These observations suggested that the molecular adsorption was primarily based on hydrogen bond interactions between the surface oxide layer on the GaN substrate and the polar functional groups of the molecules. The as-prepared ODPA monolayers were desorbed from the GaN substrates by soaking in an aqueous solution, particularly in a basic solution. However, ODPA monolayers heated at 160 degrees C exhibited suppressed desorption in acidic and neutral aqueous solution maybe due to covalent bond formation between ODPA and the surface. X-ray photoelectron spectroscopy provided insight into the effect of the UV/O 3 treatment on the surface composition of the GaN substrate and also the ODPA monolayer formation. These results demonstrate that the surface of a GaN substrate can be tailored with organic molecules having an alkylphosphonic acid moiety for future sensor and device applications.     

Generation and reactions of Pentacyclo[4.3.0.0(2,4).0(3,8).0(5,7)]non-4-ene

The highly pyramidalized alkene, pentacyclo[4.3.0.0(2,4).0(3,8).0(5,7)]non-4-ene (9), has been generated via treatment of 4,5-diiodopentacyclo[4.3.0.0(2,4).0(3,8).0(5,7)]nonane (12) with n-butyllithium and tert-butyllithium. The title alkene has also been trapped as its Diels-Alder adduct with 1,3-diphenylisobenzofuran, 2,5-dimethylfuran, and spiro[2.4]hepta-4,6-diene. Products resulting from alkyllithium addition to the pyramidalized double bond of 9 have been isolated and fully characterized spectroscopically. The geometry, olefin strain energy, heat of hydrogenation, and relative HOMO/LUMO energies of 9 have been obtained by ab initio calculations at the MP2 and B3LYP levels using the 6-31G* basis set.     

Ignition-to-spread transition of externally heated electrical wire

Ignition of electrical wires by external heating is investigated in order to gain a better understanding of the initiation of electrical-wire fires. An ignition-to-spread model is developed to systematically explain ignition and the following transition to spread. The model predicts that for a higher-conductance wire it is more difficult to achieve ignition and the weak flame may extinguish during the transition phase because of a large conductive heat loss along the wire core. An experimental study was performed using several sample wires with different core metals, diameters and coating thicknesses of polyethylene. A coil heater was adopted as the ignition source, and both the heat flux and heating time were selected as the main parameters to identify the flashpoint and spread point of wire fires. Experiments show that additional heating times after flash are required in order to fully pass the transition and achieve a spreading flame, agreeing with model predictions. Finally, the effects of different heating lengths, environmental pressures, and oxygen concentration on wire ignition are discussed, which may be useful for upgrading the design and standards of future fire-safe wires.